Dynamic Equilibrium at a Congestible Facility Under Market Power

Tinbergen Institute Discussion Paper 15-045/VIII

25 Pages Posted: 2 Apr 2015

See all articles by Erik T. Verhoef

Erik T. Verhoef

VU University Amsterdam - Department of Spatial Economics; Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Hugo Silva

VU University Amsterdam; Tinbergen Institute

Date Written: March 31, 2015

Abstract

Various contributions to the recent literature on congestion pricing have demonstrated that when services at a congestible facility are provided by operators with market power, the case in point often being a few airlines jointly using a congested airport, optimal congestion pricing rules deviate from the familiar Pigouvian rule that tolls be equal to the marginal external costs. The reason is that an operator with market power has an incentive to internalize the congestion effects that its customers and vehicles impose upon one-another, so that Pigouvian tolling would lead to overpricing of congestion. More recent contributions to this literature, however, have brought to the fore that when congestion at the facility takes on the form of dynamic bottleneck congestion à la Vickrey (1969), where trip scheduling is the key behavioural margin, there may exist no Nash e quilibrium in arrival schedules for oligopolistic operators also under rather plausible assumptions on parameters. This paper investigates whether in such cases, an equilibrium does exist for another congestion technology, namely the Henderson-Chu dynamic model of flow congestion. We find that a stable and unique equilibrium exists also in cases where it fails to exist under bottleneck congestion (notably when the value of schedule late exceeds the value of travel delays). Our results suggest that self-internalization with only two firms leads to a considerable efficiency gain compared to the atomistic equilibrium (83% or more of the gain from first-best pricing in our numerical exercises).

Keywords: Congestion pricing, dynamic congestion, market power, internalization

JEL Classification: R41, R48, D62

Suggested Citation

Verhoef, Erik T. and Silva, Hugo, Dynamic Equilibrium at a Congestible Facility Under Market Power (March 31, 2015). Tinbergen Institute Discussion Paper 15-045/VIII, Available at SSRN: https://ssrn.com/abstract=2588949 or http://dx.doi.org/10.2139/ssrn.2588949

Erik T. Verhoef (Contact Author)

VU University Amsterdam - Department of Spatial Economics ( email )

De Boelelaan 1105
1081HV Amsterdam
Netherlands
+31 020 4446094 (Phone)
+31 020 4446004 (Fax)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Hugo Silva

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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